A GENERAL ITERATIVE ALGORITHM FOR THE SOLUTION OF VARIATIONAL INEQUALITIES FOR A NONEXPANSIVE SEMIGROUP IN BANACH SPACES - Sunthrayuth, P.; Kumam, P. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2011)
Let $X$ be a uniformly convex and smooth Banach space which admits a weakly sequentially continuous duality mapping, $C$ a nonempty bounded closed convex subset of $X$. Let $S = {T(s): 0 _ 0 < ∞}$ be a nonexpansive semigroup on $C$ such that $F(S) 6= \emptyset$ and $f : C → C$ is a contraction mapping with coefficient $α \in (0, 1)$, $A$ a strongly positive linear bounded operator with coefficient $γ > 0$. We prove that the sequences ${x_t}$ and ${x_n}$ are generated by the following iterative algorithms, respectively